All Courses Math for Machine Learning : Calculus 2
Math for Machine Learning : Calculus 2
Understand and apply techniques for finding area and volume using integrals. Calculate arc length of curves and apply integration to solve related problems. Master integration techniques including integration by parts and substitution. Prove basic trigonometric identities and understand their significance in calculus. Investigate convergence of sequences and series, including power and Taylor series. Apply calculus concepts to polar coordinates and understand their geometric interpretation. Utilize numerical methods such as the trapezoid and midpoint rule for approximating integrals. Calculate slopes of parametric curves and interpret their significance in real-world scenarios.
Instructors:
SJ Sushmitha J
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55 Lessons

This course builds upon the foundations of Calculus 1, delving deeper into integral calculus and its applications. Topics include techniques for finding areas and volumes using integrals, calculating arc lengths of curves, and exploring advanced integration methods such as integration by parts and substitution. The course also covers the proofs of fundamental trigonometric identities and their role in calculus. Additionally, students will study the convergence of sequences and series, including power series and Taylor series, and their applications. Furthermore, the course extends calculus concepts to polar coordinates, numerical methods for integration, and the slopes of parametric curves. Through a combination of theoretical discussions, problem-solving exercises, and real-world applications, students will develop a solid understanding of Calculus 2 and its relevance in various fields.

Course Content
Area Between Curves
Volumes Using Cross-Sections
Volumes of Solids of Revolution
Volume of a Wedge
Volume of a Torus
Arclength
Work as an Integral
Work to pull up a Rope
Average Value of a Function
Proof of the Mean Value Theorem for Integrals
Integration by Parts
Table Method For Integration By Parts by Morgan Goetz
Trig Identity Favorites
Proof of the Angle Sum Formulas
Integrals Involving Odd Powers of Sine and Cosine
Integrals Involving Even Powers of Sine and Cosine
Special Trig Integrals
Integration Using Trig Substitution
Integrals of Rational Functions
Improper Integrals - Type 1
Improper Integrals - Type 2
The Comparison Theorem for Integrals
L'Hospital's Rule
L'Hospital's Rule on Other Indeterminate Forms
Sequences - Definitions and Notation
Sequences - More Definitions
Monotonic and Bounded Sequences Extra
Convergence of Sequences
Series Definitions
Geometric Series
Koch’s snowflake problem
The Integral Test
Comparison Test for Series
The Limit Comparison Test
Proof of the Limit Comparison Test
Absolute Convergence
The Ratio Test
Proof of the Ratio Test
Series Convergence Test Strategy
Power Series
Convergence of Power Series
Power Series Interval of Convergence Example
Proofs of Facts about Convergence of Power Series
Power Series as Functions
Representing Functions with Power Series
Taylor Series Introduction
Computing Taylor Series and Using Then to find Sums of Series
Taylor Series Theory and Remainder
Parametric Equations
Slopes of Parametric Curves
Area under a Parametric Curve
Arclength of Parametric Curves
Trapezoid Rule
Polar Coordinates
Midpoint Rule
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